Monotonicity and uniqueness of wave profiles for a three components lattice dynamical system

Chin-Chin Wu

doi:10.3934/dcds.2017121

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2017, Volume 37, Issue 5: 2813-2827. Doi: 10.3934/dcds.2017121

This issue Previous Article Existence and upper semicontinuity of random attractors for non-autonomous stochastic strongly damped wave equation with multiplicative noise Next Article Global solutions to the Chemotaxis-Navier-Stokes equations with some large initial data

Monotonicity and uniqueness of wave profiles for a three components lattice dynamical system

Chin-Chin Wu

Department of Applied Mathematics, National Chung Hsing University, 145, Xingda Road, South Dist, Taichung 402, Taiwan

Received: May 2016

Revised: December 2016

Published: May 2017

This work was partially supported by the Ministry of Science and Technology of the Republic of China under the grant 105-2115-M-005-002. The author would like to thank the referees for valuable comments.

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Abstract

We consider a three components lattice dynamical system which arises in the study of a three species competition model. It is assumed that two weaker species have different preferences of food and the third stronger competitor has both preferences of food. Under this assumption, it is well-known that there is the minimal speed such that a traveling wave solution exists for any speed above this minimal one. In this paper, we prove the monotonicity of wave profiles and the uniqueness (up to translations) of wave profiles for each given admissible speed under certain restrictions on parameters.

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Mathematics Subject Classification: Primary: 34K05, 34A34; Secondary: 34K60, 34E05.

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